Conventional optical holography constructs a volume (three dimensional) image of an object by displaying the amplitude and the phase structure of a wavefront of light. A reference wave of light is relied upon to facilitate the recording of both the amplitude and the phase condition of the object light by means of photographic emulsion. This reference wave is coherent with the object light and interferes with it, producing diffraction patterns which form an optical hologram on the photographic emulsion. To generate a volume image, this optical hologram need merely be illuminated with a reference light wave. The resulting diffraction pattern wave (as scattered by the emulsion) is identical to the original wavefront of light scattered by the object, and therefore reproduces the volume image of the object.
U.S. Pat. No. 3,887,923 to Hendrix discloses an application of the principles of optical holography within the radio-frequency domain. The '923 patent discloses a passive radio direction finder which monitors the amplitude and phase of radio-frequency wave fronts across an aperture. An array of antennas sample the phase of incoming wave fronts. Each antenna is associated with a mixer, and one of the antennas provides a mixer reference signal for an input to each mixer. The signals are processed through an analog-to-digital converter and a computer programmed rapidly to execute Fourier transforms, eventually to produce a numerical reconstruction of the radio frequency hologram.
U.S. Pat. No. 5,299,033 to Leith, et al discloses a method whereby an image of an object embedded in a diffusing medium is formed by propagating a coherent light pulse through the diffusing medium and applying a reference pulse to gate precisely the first emerging light transmitted through the diffusing medium. To produce an image, it is necessary for the diffusing medium to be transparent, because the method relies upon optical light.
There have been several attempts to develop an imaging method, utilizing a low frequency electromagnetic (EM) field, especially as applied to the solution of geophysical problems. K. H. Lee and G. Xie, in both U.S. Pat. No. 5,373,443 and the article, “A new approach to imaging with low-frequency electromagnetic fields,” Geophysics, volume 58, pages 780-796 (1993), describe a method for imaging electrical conductivity with low-frequency electromagnetic fields, using wavefield transforms and ray tomography. This work has recognized a relationship between low frequency diffusion EM field equations and wave equations, but practical applications of this method have been directed to defining interfaces, rather than three dimensional imaging.
In the article entitled “Continuation of the transient electromagnetic field in the geoelectrical problems,” Physics of the Earth (Izvestia Akademy Nauk—in Russian), No. 12, pages 60-69, 1981, the present inventor presented a mathematical transform, based upon the theory of Stratton-Chu integrals, of the field recorded on the earth's surface and scattered from a subsurface geological object downward to locate and image the object. Subsequently, the present inventor and M. A. Frenkel coauthored an article entitled “The solution of the inverse problems on the basis of the analytical continuation of the transient electromagnetic field in reverse time,” J. Geomagn. Geolelectr., volume 35, pages 747-765 (1983), which developed this method and introduced an imaging concept based upon downward extrapolation of an EM field in reverse time (electromagnetic migration).
The inventor has further coauthored the articles: “Resistivity Imaging by Time Domain Electromagnetic Migration (TDEMM)” (with P. Traynin and O. Portniaguine), Exploration Geophysics, volume 26, pages 186-194 (1995), reporting work which tested the imaging concept using controlled-source electromagnetic data, with limited success for two-dimensional models only, and “Underground Imaging by Frequency Domain Electromagnetic Migration,” (with P. Traynin and J. R. Booker), Geophysics, volume 61, No. 3, pages 666-682 (1996), explaining application of the migration method to natural EM field geophysical data interpretation, but this study was limited to two-dimensional magnetotelluric problems.
These earlier efforts to develop a method for quickly interpreting geophysical EM data over two-dimensional geoelectrical structures have met with limited success. Moreover, they have not pointed towards a practically useful method for accomplishing broad band EM imaging of three-dimensional objects in nontransparent media. There remains a need for a method of imaging capable of providing the volume image of objects located in nontransparent media similar to images produced by optical or radio-wave holography. Such a method would be useful in geophysical exploration, in environmental study (for example, in searching for buried mines), for nondestructive detection of defects in metal and in medical applications (for example, in breast cancer or diseased bone diagnoses).